Question: In Chapter 34, we will model particle diffusion as a random walk in one dimension. In such processes, the probability of moving an individual step

In Chapter 34, we will model particle diffusion as a random walk in one dimension. In such processes, the probability of moving an individual step in the +x or −x direction is equal to one half. Imagine starting at x = 0 and performing a random walk in which 20 steps are taken.

a. What is the farthest distance the particle can possibly move in the +x direction? What is the probability of this occurring?

b. What is the probability the particle will not move at all?

c. What is the probability of the particle moving half the maximum distance in the x direction?

d. Plot the probability of the particle moving a given distance versus distance. What does the probability distribution look like? Is the probability normalized?

Step by Step Solution

★★★★★

3.51 Rating (174 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The problem of a random walk is just like the cointoss example discussed in the text and which ser... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Physical Chemistry Questions!

In Chapter 19 we will see that a charged particle can undergo uniform circular motion when acted on by a magnetic force and no other forces. (a) For that to be true, what must be the angle between...

Consider a single, porous, spherical, inert mineral particle. The pores inside the particle are filled with liquid water (species B). We are interested in analyzing the molecular diffusion of the...

We are interested analyzing the diffusion processes associated with the treatment of cancer cells. Consider the experimental system shown in the figure on page 524. A hemispherical clump of cancer...

Problem 1 [A Few Random Steps} Consider four molecules, all starting at the origin, which undergo a 1d random walk, each with a 50% chance of going left or right along the x-axis at each time step....

I need this in c programming the assignment is given and also code is given you just have to code the lines where it says TODO here please edit the code that I have given and please send me a...

The behaviour of a particle in a gas can be considered to behave like a random walker. In one dimension, the final position 2y of a random walker after N steps can be found by adding each of the...

#includ #include #include / / TODO / / Implement the below function / / Simulate one particle moving n steps in random directions / / Use a random number generator to decide which way to go at every...

2.7. Explicit Solutions to Dierential Equations 109 power (kw) 20 15 10 5 0 08:00 10:00 12:00 14:00 16:00 time 18:00 2.7 Explicit Solutions to Dierential Equations In the very rare case in which an...

HOMEWORK 4 1. Exercises All exercises and examples are from [D], Chapter 6 (Markov Chains), with the corresponding numbering (e.g. Exercise 6.4.5). Exercise 1. Write down the one-step transition...

Shortly after moving into the new home, Kate started a new business called Kates Beauty Cuts LLC. She set up shop in a 384-square-foot corner room of the couples home and began to get it ready for...

Discuss the differences between centralized and decentralized decision making.

You want to invest $ 1 million in the hedge fund. It's currently August 6 , 2 0 2 1 . When can you invest? January 1 , 2 0 2 2 September 1 , 2 0 2 1 October 1 , 2 0 2 1 August 7 , 2 0 2 1

If Leisure Island produces 4 shows and 9 meals a week, is production efficient?

At what temperature is the standard molar entropy of helium equal to that of xenon at 298K?

Evaluate, by explicit summation, the mean vibrational energy of CS 2 and plot its value as a function of temperature. At what temperature is the equipartition value within 5 per cent of the accurate...

The rotational constant of CH 4 is 5.241 cm 1 . Evaluate the rotational partition function explicitly (without approximation but ignoring the role of nuclear statistics) and plot its value as a...

i need help For each scenario, list all the numberls) ofany of the diagrams that could satisfy the given situation.There may be more than one diagram satisfying a situation which means you magir be...

Goodwin Technologies has been wildly successful but has yet to pay a dividend. An analyst forecasts that Goodwin is likely to pay its first dividend three years from now. She expectes Goodwin to pay...

How many different ID cards can be made if there are three digits on a card and no digit can be used more than once? What if digits can be repeated?